INGEBRETSON-DISSERTATION-2018.pdf (2.63 MB)
0/0

Hausdorff Dimension of Kuperberg Minimal Sets

Download (2.63 MB)
thesis
posted on 27.11.2018 by Daniel Ingebretson
In 1994, Kuperberg constructed a smooth flow on a three-manifold with no periodic orbits. It was later shown that a generic Kuperberg flow preserves a codimension one laminar minimal set. We develop new techniques to study the symbolic dynamics and dimension theory of this minimal set, by relating it to the limit set of a graph directed pseudo-Markov system over a countable alphabet.

History

Advisor

Hurder, Steve

Chair

Hurder, Steve

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Furman, Alex Culler, Marc Rechtman, Ana Lukina, Olga

Submitted date

August 2018

Issue date

27/07/2018

Exports

Categories

Exports